The blood cells without nuclei are erythrocytes or Red blood cells. When the RBCs are developing in the red bone marrow, they do have nuclei. However, these nuclei are ejected from the cells when they enter the bloodstream in a process known as enucleation. The advantage for this condition is the nucleus takes up a lot of space in a cell. This space can be used to fit in more hemoglobin. Hence, to carry oxygen more efficiently, RBCs don't have a nucleus.